= Two-state RNA melting model
A \b[two-state RNA melting model] treats an RNA transition as an equilibrium between folded F and unfolded U macrostates, with no substantially populated intermediate. Each macrostate can contain many microscopic conformations; two states does not mean exactly two atom-by-atom structures. The model relates populations to thermodynamics and then, separately, to an observed optical signal.
For unfolding free energy $\Delta G_u=G_U-G_F$,
$$
K_u=\frac{f_U}{1-f_U}=e^{-\Delta G_u/(RT)},\qquad
f_U=\frac{1}{1+e^{\Delta G_u/(RT)}}.
$$
The population formula assumes an ideal unimolecular transition. With constant unfolding enthalpy and entropy,
$$
\ln\frac{f_U}{1-f_U}=-\frac{\Delta H_u}{RT}+\frac{\Delta S_u}{R}.
$$
An <RNA melting log-odds plot> against $1/T$ is then a straight line. Nonzero changes in <heat capacity>, alternative states or incorrect population estimates can invalidate this simplified relation.
An original consistency test fits stipulated $f_U=0.10$ at $300\,\mathrm K$ and $f_U=0.50$ at $330\,\mathrm K$. These two points determine
$$
\frac{\Delta H_u}{R}=\frac{\ln9}{1/300-1/330},\qquad
\Delta S_u=\frac{\Delta H_u}{330\,\mathrm K}.
$$
The fitted model predicts approximately $f_U=0.862$ at $360\,\mathrm K$. A third observation tests that prediction; fitting two parameters to two points was not independent validation. Measurement uncertainty and baselines must be considered before attributing disagreement to a specific physical mechanism.
For an ideal optical mixture, $A(T)=[1-f_U(T)]A_F(T)+f_U(T)A_U(T)$. Thus the population model does not remove the need for folded and unfolded <RNA melting baselines>. Optical-melting studies infer thermodynamics by fitting measured curves under stated analysis assumptions.<Thermodynamic characterization of naturally occurring RNA tetraloops by Justin P. Sheehy and others>[Materials and Methods, optical curves and individual-curve thermodynamic fitting.]{ref}
Reversibility, the absence of important intermediates and the unimolecular assumption are physical conditions to test. A two-strand association transition has a different concentration dependence even if its optical trace looks similarly sigmoidal. The model is a useful quantitative hypothesis, not a consequence of drawing one smooth curve through data.
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